Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
740 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×Dic1004 | C2 | semidirect |
| 3. C22×#16860800 | C2 | semidirect |
| 5. #30631844 | C2 | direct (N × H) |
| 6. C2×#22548638 | C2 | semidirect |
| 8. C2×#103×C251 | C2 | semidirect |
| 19. C2×Dic1004 | C22 | semidirect |
| 21. C2×#16860800 | C22 | semidirect |
| 27. #22548638 | C22 | semidirect |
| 32. #103×C251 | C22 | semidirect |
| 75. C22×D251 | Q16 | semidirect |
| 115. C2×D251 | C2×Q16 | semidirect |
| 124. C2×C251 | #451 | semidirect |
| 129. C251 | C2×#451 | semidirect |
| 137. C2×#103 | D251 | semidirect |
| 161. #103 | C2×D251 | semidirect |
| 255. C2 | #30631844 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D251 | 2 |
| C22×Dic1004 | 2 |
| C22×#16860800 | 2 |
| C2×#22548695 | 2 |
| #30631844 | 2 |
| C2×#22548638 | 2 |
| C2×(C2×D251)⋊C8 | 2 |
| C2×#103×C251 | 2 |
| C2×#451 | 251 |